Question

tìm hai số nguyên dương a,b biết ab=180,BCNN[a,b]=60

 

Answer 1

giúp với ạ

 

Answer 2

\(ab=180;BCNN\left(a;b\right)=60\)

\(ab=BCNN\left(a;b\right).UCLN\left(a;b\right)\)

\(\Rightarrow UCLN\left(a;b\right)=\dfrac{180}{60}=3\)

Đặt \(a=3x;b=3y\) \(\left(x;y>0\right)\)

\(\Rightarrow xy=\dfrac{180}{3.3}=20\)

\(\Rightarrow\left(x;y\right)=\left(1;20\right);\left(2;10\right);\left(4;5\right);\left(5;4\right);\left(10;2\right);\left(20;1\right)\)

\(\Rightarrow\left(a;b\right)=\left(3;60\right);\left(6;30\right);\left(12;15\right);\left(15;12\right);\left(30;6\right);\left(60;3\right)\)